Fluorite-type materials in the monolayer limit

The 2H, 1T, and their distorted structures are known as prototype structures of $A{B}_{2}$ monolayers. Here, we study a puckered (PCK) structure that is truncated from the (110) surface of fluorite-type materials. 53 fluorite-type materials are investigated based on first-principles approach. The formation energy calculations indicate that seven systems form the PCK structure in the monolayer limit, while other systems form either 1T, 2H, or distorted 1T structures. The PCK structures of ${\mathrm{PbF}}_{2}$ and ${\mathrm{Ga}}_{2}\mathrm{Au}$ exhibit negative Poisson's ratio (NPR) in the out-of-plane direction. We explain the NPR by an analytical model assuming a constant interatomic distance under the in-plane strain. In addition, we demonstrate that the appearance of NPR is correlated with non-ionic character of the system, which is based on the surface energy calculations and the Born effective charge analyses. We also find that ${\mathrm{PRh}}_{2}$ in the PCK structure is highly distorted.